Question

Question 1: Identify the number and type of solutions for the equation x2 − 7x + 3 = 0. Answers: 2 real, 1 real, 1 nonreal complex, 2 nonreal complex Question 2: Identify the number and type of solutions for the equation 3x2 + 2x + 9 = 0. Answers: 1 nonreal complex, 2 real, 1 real, 2 nonreal complex

Answer 1

Answer:

below

Step-by-step explanation:

$x^{2} -7x + 3$

this is a quadratic equation so we will use the quadratic formula to solve it

• a = 1
• b = -7
• c = 3

The quadratic formula:

• b² - 4ac = (-7)²-4*1*3 = 37
• 37 is a positive number so the equation has two solutions

$x = \frac{-b + / - \sqrt{37} }{2a}$ ⇒ $x = \frac{7 + / - \sqrt{37} }{2}$

                      ⇒ $\left \{ {{x=0.45} \atop {x=6.54}} \right.$

The solutions are 2 real numbers